In this paper, we introduce a new extension in the subject of fuzzy metric, called controlled fuzzy metric space. This notion is a generalization of fuzzy b-metric space. Also, we prove a Banach-type fixed point theorem and a new fixed point theorem for some self-mappings satisfying fuzzy-contraction condition that is more general than existing theorems. Furthermore, we establish some examples about our main results.
In this paper, we introduce some new concepts of contractions calledγ-contractions andγ-weak contractions. We prove some fixed point theorems for mappings providingγ-contractions andγ-weak contractions unlike known results in the literature. Also, we present a few examples to illustrate the validity of the results obtained in the paper.
In this work, we prove a new fixed point theorem in the setting fuzzy metric spaces. The fuzzy metric space considered here is assumed to have two partial orders defined on it. We introduce a new approach to the existence of a fixed point of a function satisfying the two constraint inequalities. An example is included which illustrates new results of this paper. Moreover, an application of our result to the study of integral equations is provided.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.